Short Communications

On the representation of certain classes of stochastic Ito integrals in the form of pathwise Lebesgue integrals

F. S. Nasyrov

Ufa State Aviation Technical University

Abstract: We obtained a representation of the Ito integral in the form of the Lebesgue integral and a generalization of the Ito formula. It is proved that a monotone permutation of paths of the Wiener process is absolutely continuous.

Keywords: Ito integral, local times, Ito formula.

Received: 17.12.1996
Revised: 15.07.1998

DOI: 10.4213/tvp780

 English version: Theory of Probability and its Applications, 2000, 44:2, 404–409

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